Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)at...Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.展开更多
In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying ...In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying an appropriate fixed point theorem and Lyapunov functional method.Finally,a numerical example with simulation is given to illuminate our theoretical results.展开更多
在解析数论领域,探讨全纯尖形式的傅里叶系数具有重要的理论价值.通过复变函数的积分技巧,结合自守L-函数的凸界以及积分均值估计方法,研究了不同序列上傅里叶系数的一致均值估计,形式化表达为∑n≤xλf nλf n j,j=2,3,其中f是全模群Γ...在解析数论领域,探讨全纯尖形式的傅里叶系数具有重要的理论价值.通过复变函数的积分技巧,结合自守L-函数的凸界以及积分均值估计方法,研究了不同序列上傅里叶系数的一致均值估计,形式化表达为∑n≤xλf nλf n j,j=2,3,其中f是全模群Γ=SL(2,Z)上权为偶数k的Hecke特征型,λf n是其在尖点∞处傅里叶展开的第n个标准化傅里叶系数.展开更多
Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1,...Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).展开更多
文摘Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.
文摘In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying an appropriate fixed point theorem and Lyapunov functional method.Finally,a numerical example with simulation is given to illuminate our theoretical results.
文摘在解析数论领域,探讨全纯尖形式的傅里叶系数具有重要的理论价值.通过复变函数的积分技巧,结合自守L-函数的凸界以及积分均值估计方法,研究了不同序列上傅里叶系数的一致均值估计,形式化表达为∑n≤xλf nλf n j,j=2,3,其中f是全模群Γ=SL(2,Z)上权为偶数k的Hecke特征型,λf n是其在尖点∞处傅里叶展开的第n个标准化傅里叶系数.
基金This work is supported by NSF of China NSF of Heilongjiang province
文摘Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).
